Nonmetric ANOVA: a generic framework for analysis of variance on dissimilarity measures

Abstract

Classic analysis of variance (ANOVA; cA) tests the explanatory power of a partitioning on a set of objects. Nonparametric ANOVA (npA) extends to a case where instead of the object values themselves, their mutual distances are available. While considerably widening the applicability of the cA, the npA does not provide a statistical framework for the cases where the mutual dissimilarity measurements between objects are nonmetric. Based on the central limit theorem (CLT), we introduce nonmetric ANOVA (nmA) as an extension of the cA and npA models where metric properties (identity, symmetry, and subadditivity) are relaxed. Our model allows any dissimilarity measures to be defined between objects where a distinctiveness of a specific partitioning imposed on those are of interest. This derivation accommodates an ANOVA-like framework of judgment, indicative of significant dispersion of the partitioned outputs in nonmetric space. We present a statistic which under the null hypothesis of no differences between the mean of the imposed partitioning, follows an exact F-distribution allowing to obtain the consequential p-value. Three biological examples are provided and the performance of our method in relation to the cA and npA is discussed.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

* https://github.com/AmiryousefiLab/nmANOVA